Covariance Matrix Adaptation Evolution Strategy Assisted by Principal Component Analysis

TL;DR

This paper introduces a PCA-assisted covariance matrix adaptation evolution strategy (CMA-ES) to improve convergence in high-dimensional black-box optimization problems by reducing computational complexity.

Contribution

The paper proposes integrating PCA into CMA-ES to enhance its efficiency and scalability for high-dimensional problems, validated on benchmark datasets.

Findings

Improved convergence rate on multi-modal problems

Reduced computational cost in high dimensions

Competitive performance compared to existing algorithms

Abstract

Over the past decades, more and more methods gain a giant development due to the development of technology. Evolutionary Algorithms are widely used as a heuristic method. However, the budget of computation increases exponentially when the dimensions increase. In this paper, we will use the dimensionality reduction method Principal component analysis (PCA) to reduce the dimension during the iteration of Covariance Matrix Adaptation Evolution Strategy (CMA-ES), which is a good Evolutionary Algorithm that is presented as the numeric type and useful for different kinds of problems. We assess the performance of our new methods in terms of convergence rate on multi-modal problems from the Black-Box Optimization Benchmarking (BBOB) problem set and we also use the framework COmparing Continuous Optimizers (COCO) to see how the new method going and compare it to the other algorithms.